Answer:
To find the missing side length in triangle EDF, John can't use the Pythagorean theorem due to the angle not being 90 degrees. Using the Law of Cosines, he finds that \( DF \) is approximately 37.5 cm.
Step-by-step explanation:
To determine the missing side length in triangle EDF, John can use the Law of Cosines since the angle between the known sides is not 90 degrees. The Law of Cosines states that \( c^2 = a^2 + b^2 - 2ab \cdot \cos(C) \), where \( c \) is the side opposite angle \( C \) and \( a \) and \( b \) are the other two sides.
Given \( EF = 25 \) cm, \( ED = 23 \) cm, and angle \( E = 91^\circ \), to find \( DF \), we can use the Law of Cosines:
\( DF^2 = ED^2 + EF^2 - 2 \cdot ED \cdot EF \cdot \cos(E) \)
\( DF^2 = 23^2 + 25^2 - 2 \cdot 23 \cdot 25 \cdot \cos(91^\circ) \)
\( DF^2 = 529 + 625 - 2 \cdot 23 \cdot 25 \cdot (-0.448) \)
\( DF^2 = 529 + 625 + 252.8 \)
\( DF^2 = 1406.8 \)
\( DF = \sqrt{1406.8} \)
\( DF ≈ 37.5 \) cm
So, the missing side length \( DF \) is approximately 37.5 cm.
